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Compute
4 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4}}}}

 Jul 16, 2024
 #1
avatar+1926 
+1

Let's work from bottom up. Starting with the smallest, we have \(\frac{1}{\frac{17}{4}}=\frac{4}{17}\)

Then, we have \(4+\frac{4}{17}=\frac{72}{17}\)

\(4+\frac{1}{4+\frac{1}{4}}=\frac{72}{17}\)

 

Thus, we have

\(\frac{1}{4+\frac{1}{4+\frac{1}{4}}}=4+\frac{17}{72}=\frac{305}{72}\)

 

The final answer is \(\frac{305}{72}\)

 Jul 16, 2024
edited by NotThatSmart  Jul 16, 2024

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